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Interpreting Carry and Roll-Down in SOFR Swaps

Article Quant Q&A · Author: swissy
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Summary

The discussion questions how to define carry for a fixed-for-floating SOFR swap when its compounded floating payment is not known in advance. One answer argues that a simple difference between the next fixed and floating payments is not a useful standalone measure: the expected cash flows over the full swap and the curve shape matter. It illustrates this with two- and three-year swaps, showing that differences in early-period rates are offset by the rates implied for later periods.

A second response describes a horizon-based carry calculation for a longer swap using forward-starting swap rates and relative DV01s. Together, the answers distinguish carry from roll-down and show that terminology and calculation can depend on the measure being used. The exchange does not establish a single agreed definition; it presents competing perspectives and relies on approximate curve-based reasoning rather than a worked valuation framework.

Key ideas

  • A swap’s first-period fixed-floating difference does not capture its full expected cash-flow profile.
  • Curve shape and later-period rates help explain the economics of a swap’s initial cash flows.
  • One response treats paper interest-rate swaps as having zero expected cost of carry and separates roll-down from carry.
  • Another response gives a horizon-based carry expression using forward-starting swap rates and DV01s.
  • The discussion reflects differing definitions rather than a settled convention.

Tags

Fixed incomeCarryDerivatives pricing
Full text
# Carry of a SOFR swap


# Carry of a SOFR swap












This might be a stupid question, but I'm wondering about the following. The SOFR swaps are usually structured to make regular payments on a yearly basis, fixed for floating. The fixed rate is simply the agreed coupon rate. However, the floating rate will be the compounded SOFR rate over that year that is not know in advance. My understanding is, that the carry of a swap is calculated as the the difference of the next fixed and floating payment. But since I don't know the floating yet, is there a concept of carry for these swaps? One could take implied fwd rates from the market, but that would not accurately count as carry as this might change. Thanks for claryfication

## Answer by Attack68 (score 2, accepted)

https://quant.stackexchange.com/a/80974

No. I don't define the "carry" of a swap like this. Not on the job, and not in my book (Pricing and Trading Interest Rate Derivatives: a practical guide to swaps). Actually I claim that IRS like this (as paper contracts) have an expected cost-of-carry of zero. (Roll-down is another calculation entirely).

The value to which you refer, which I have no name for, in my view, is a useless metric, and I have never used it.

Suppose you look at the current US SOFR curve:

```
1y: 4.15%
2y: 3.84%
3y: 3.74%
1y1y: 3.52%
```

If you receive a 2y swap at 3.84%, the "difference between that and the first (1y) period" is -31bps. What does this indicate? Not a whole lot other than the second half of the swap must have expected lower rates to recoup the initial cash outflow. And it does: the 1y1y is 3.52%.

If you receive a 3y swap at 3.74%, the "difference between that and the first (1y) period" is -41bps. Again, very little additional information.

You can get the same amount of information by asking the question: what are the expected net cashflows on these swaps? (approximately)

2Y (1mm notional): -3.25k, +3.25k

3Y (1mm notional): -4.2k, +2.1k, +2.1k

You don't lose (or earn) money simply due to the first cashflow. You have to factor in the whole curve.

## Answer by user68819 (score 0)

https://quant.stackexchange.com/a/80917

Let's take the carry of a 10y sofr swap with a horizon of 1y.

This would be 1y9y - 10y = (10y -1y) x dv01 (1y)/ dv01 (1y9y)

If the carry were not exactly this number I could either pay 1y9y rec 10y or vice versa and make money for free.

There is no difference between this and a LIBOR swap for eg, as you can lock the 1y spot start swap in today in this example (approx as the first fixing is already known in a 1y spot start swap)

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.